Rome, Italy (CNN) -- Alleged victims of child abuse by Catholic priests in Ireland called on the Vatican Monday to hold its own investigation into the scandal and punish those responsible.

"We ask that you take action now according to the laws and traditions of our Holy Church and discover how and why the teachings of Jesus Christ were so flagrantly abrogated over many decades," John Kelly said in a letter to Pope Benedict XVI.

"We ask that you convene a special commission ... to examine all aspects of the historical misconduct of Catholic religious orders in Ireland as well as those priests who betrayed their most sacred vows," he said.

Kelly, the founder of Survivors of Child Abuse, or SOCA, released the letter as Irish Catholic bishops met the pope in Rome after a damning report on the abuse of children by Catholic clergy.

The report, which came out in November, found that the Catholic Church in Ireland covered up widespread child abuse from 1975 to 2004.

The pope already has met with senior Irish bishops about the report, produced by the Dublin Archdiocese Commission of Investigation. The Irish government created the commission in 2006 to examine abuse allegations.

The Vatican now needs to order a major housecleaning, Kelly told CNN.

"They need to clean the stables up. They need to inquire into all the bishops, and if that means the majority of them would have to resign, then so be it," Kelly said.

"The bishops themselves are the problem. Somebody has dishonored this nation," said Kelly, who says he was himself abused in a Catholic institution in Dublin, Ireland, as a child.

"Nobody has been locked up or prosecuted for these crimes in Ireland," he said, saying it is now the Vatican's responsibility to punish the guilty. "The pope could do an awful lot if he is sincere.

"We are entitled to have great expectations," he told CNN by phone from Ireland. "I want strong leadership from the pope."

"We are asking the curia to examine the facts before them," said Patrick Walsh of SOCA, using a term for the leadership of the Catholic church.

"This is not a time for high Mass. That time is finished," he said. "It is time to pass judgment under Roman law."

The Irish Catholic bishops attended Mass in Rome on Monday morning before meeting with the pope. Benedict did not attend the Mass, his spokesman, Father Federico Lombardi, told CNN.

Cardinal Tarcisio Bertone, the Vatican secretary of state, presided, and addressed the scandal directly in his homily, calling the alleged abuse "abominable acts."

"Trials can come from either outside or inside the church. Both are painful, but those that come from within are naturally harder and more humiliating," he said, according to Lombardi.

"Such is the grave trial that at this moment your communities are going through, which see some men of the church involved in such particularly abominable acts," he said.

The Irish bishops prayed for the victims, said their spokesman, Martin Long.

"Prayers were offered to the survivors of abuse, the people, priests, and religious of Ireland. Prayers were also offered for the success of the meeting," he said.

One of the bishops meeting the pope said Sunday that the church in Ireland had been badly damaged by the revelations of abuse and cover-up.

"I would admit quite frankly what everybody else knows, shouted from housetops, that the church has been seriously wounded," Bishop Joseph Duffy said in Rome.

"This has done an immense damage to the authority of the church as the mouthpiece of the gospel of Jesus Christ. Of that there is no doubt," he said.

Each of the bishops will have seven minutes to speak at the meeting with the pontiff, Duffy said. The meeting was to go on all day Monday and resume Tuesday morning.

The bishops are staying at the Vatican, in the same hotel the cardinals of the church used when they last chose a new pope.

Benedict last week reiterated the Vatican's condemnation of child abuse.

"Unfortunately, in various instances, some [church] members, acting in contradiction with these commitments, have violated [children's] rights: a behavior that the church has not ceased to -- and will never cease to -- deplore and condemn," he said February 8.

The pope said after that meeting that he was "deeply disturbed and distressed" by the report's findings. He promised that the Catholic Church would try to develop strategies to make sure abuses don't happen again.

"He wishes once more to express his profound regret at the actions of some members of the clergy who have betrayed their solemn promises to God, as well as the trust placed in them by the victims and their families, and by society at large," the Vatican said in a statement then.